4(a^2+11a-48)=0

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Solution for 4(a^2+11a-48)=0 equation: 


Simplifying
4(a2 + 11a + -48) = 0

Reorder the terms:
4(-48 + 11a + a2) = 0
(-48 * 4 + 11a * 4 + a2 * 4) = 0
(-192 + 44a + 4a2) = 0

Solving
-192 + 44a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-48 + 11a + a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-48 + 11a + a2)' equal to zero and attempt to solve:

Simplifying
-48 + 11a + a2 = 0

Solving
-48 + 11a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 11a + 48 + a2 = 0 + 48

Reorder the terms:
-48 + 48 + 11a + a2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 11a + a2 = 0 + 48
11a + a2 = 0 + 48

Combine like terms: 0 + 48 = 48
11a + a2 = 48

The a term is 11a.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11a + 30.25 + a2 = 48 + 30.25

Reorder the terms:
30.25 + 11a + a2 = 48 + 30.25

Combine like terms: 48 + 30.25 = 78.25
30.25 + 11a + a2 = 78.25

Factor a perfect square on the left side:
(a + 5.5)(a + 5.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(a + 5.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
a + 5.5 = 8.845903006

Simplifying
a + 5.5 = 8.845903006

Reorder the terms:
5.5 + a = 8.845903006

Solving
5.5 + a = 8.845903006

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-5.5' to each side of the equation.
5.5 + -5.5 + a = 8.845903006 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + a = 8.845903006 + -5.5
a = 8.845903006 + -5.5

Combine like terms: 8.845903006 + -5.5 = 3.345903006
a = 3.345903006

Simplifying
a = 3.345903006


Subproblem 2
a + 5.5 = -8.845903006

Simplifying
a + 5.5 = -8.845903006

Reorder the terms:
5.5 + a = -8.845903006

Solving
5.5 + a = -8.845903006

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-5.5' to each side of the equation.
5.5 + -5.5 + a = -8.845903006 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + a = -8.845903006 + -5.5
a = -8.845903006 + -5.5

Combine like terms: -8.845903006 + -5.5 = -14.345903006
a = -14.345903006

Simplifying
a = -14.345903006


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.345903006, -14.345903006}
Solution
a = {3.345903006, -14.345903006}

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